A Behavioral Micro-foundation for Cross-sectional Network Models

Models for cross-sectional network data have become increasingly well-developed in recent decades, and are widely used. This has led to a growing interest in the connection between such cross-sectional models and the behavioral processes from which the corresponding networks were presumably generated. Here, we build on prior work in this area to present a behavioral micro-foundation for cross-sectional network models, based on a continuous time stochastic choice mechanism, that can accommodate highly general classes of cases (including agents who are not themselves in the network, and multilateral edge control). As we show, the equilibrium behavior of this process under appropriate conditions can be expressed in exponential family form, allowing estimation of individual preferences using existing methods; the graph potential separates naturally into a preference-based term reflecting agent utilities, and an entropic term reflecting the rules of tie formation. We illustrate our approach via an analysis of friendship in a professional organization, and modeling of phase transitions in the structure of small groups.